Cameron wants to double the UK's trade with the emerging economic giant by 2015.

He also sent out a message to young Indians that they should not be deterred from applying to study in the UK by the coalition's immigration clampdown.

David Cameron plays cricket in Delhi during his last trip to India

Admitting that the Government "haven't perhaps communicated this properly" to would-be students, he stressed there was "no limit" on the numbers of Indians studying at British universities or staying on in graduate-level jobs.

He told Zee TV how he had spent "fantastic holidays" in Kerala and treasured a signed cricket bat given to him by Sachin Tendulkar.

The visit will take in capital New Delhi and commercial centre Mumbai.

Cameron acknowledged that the Conservative Party has "still got work to do" to attract voters of Indian heritage in the UK.

He insisted that his party's values of "belief in family, belief in entrepreneurship, belief in the importance of neighbourhood and community" were similar to those of many members of the Indian community in Britain, but admitted that "in the past we weren't open enough".

He said he was "proud" that there were now Sikh and Hindu Tories in Parliament and wanted to do more to recognise the contribution of the Indian community to society.

And he steered carefully clear of appearing to interfere in the vexed issue of rival Indian and Pakistani claims to the territory of Kashmir.